Open AccessThe Sunyaev–Zel'dovich angular power spectrum as a probe of cosmological parameters
Author(s) -
Komatsu E.,
Seljak U.
Publication year - 2002
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2002.05889.x
Subject(s) - physics , astrophysics , spectral density , galaxy cluster , halo , cluster (spacecraft) , cosmology , matter power spectrum , dark matter , radius , cold dark matter , dark energy , galaxy , statistics , mathematics , computer security , computer science , programming language
The angular power spectrum of the Sunyaev–Zel'dovich (SZ) effect is a powerful probe of cosmology. It is easier to detect than individual clusters in the field, is insensitive to observational selection effects and does not require a calibration between cluster mass and flux, reducing the systematic errors that dominate the cluster‐counting constraints. It receives a dominant contribution from virialized cluster region between 20 and 40 per cent of the virial radius and is thus relatively insensitive to the poorly known gas physics in the cluster centre, such as cooling or (pre)heating. In this paper we derive a refined analytic prediction for the SZ angular power spectrum using the universal gas density and temperature profile and the dark matter halo mass function. The predicted power spectrum has no free parameters and fits all of the published hydrodynamic simulation results to better than a factor of 2 for 2000 < l < 10 000 . We find that the angular power spectrum C l scales as C l ∝σ 7 8 (Ω b h ) 2 and is almost independent of all of the other cosmological parameters. This differs from the local cluster abundance studies, which give a relation between σ 8 and Ω m . We also compute the covariance matrix of C l using the halo model and find a good agreement relative to the simulations. We argue that the best constraint from the SZ power spectrum comes from l ∼ 3000 , where the sampling variance is sufficiently small and the spectrum is dominated by massive clusters above 10 14 h −1 M ⊙ for which cooling, heating and details of star formation are not very important. We estimate how well we can determine σ 8 (Ω b h ) 2/7 with sampling‐variance‐limited observations and find that for a several‐square‐degree survey with arcmin resolution one should be able to determine σ 8 to within a few per cent, with the remaining uncertainty dominated by theoretical modelling. If the recent excess of the cosmic microwave background power on small scales reported by Cosmic Background Imager (CBI) and Berkeley Illinois Maryland Association (BIMA) experiments is due to the SZ effect, then we find σ 8 (Ω b h /0.035) 0.29 = 1.04 ± 0.12 at 95 per cent confidence level (statistical) and with a residual 10 per cent systematic (theoretical) uncertainty.